Let (mathscr{A}=sigma(mathscr{G})) be a (sigma)-algebra on (X), where (mathscr{G}=left{G_{i}: i in mathbb{N}ight}) is a countable generator. Let
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Let \(\mathscr{A}=\sigma(\mathscr{G})\) be a \(\sigma\)-algebra on \(X\), where \(\mathscr{G}=\left\{G_{i}: i \in \mathbb{N}ight\}\) is a countable generator. Let \(g:=\sum_{i=1}^{\infty} 2^{-i} \mathbb{1}_{G_{i}}\). Show that \(\sigma(g)=\mathscr{A}\).
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For every n E IN the function n 8 x 21G x X E X i1 is AB Rmeasurable Therefore g l...View the full answer
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